All language subtitles for 012 Continuous Distributions The Chi-Squared Distribution_en

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Would you like to inspect the original subtitles? These are the user uploaded subtitles that are being translated: 1 00:00:03,030 --> 00:00:04,380 Instructor: Welcome back, folks. 2 00:00:04,380 --> 00:00:05,970 This is going to be a short lecture 3 00:00:05,970 --> 00:00:08,823 where we introduce you to the chi-squared distribution. 4 00:00:09,780 --> 00:00:13,200 For starters, we denote a chi-squared distribution 5 00:00:13,200 --> 00:00:16,560 as the capital Greek letter chi squared 6 00:00:16,560 --> 00:00:21,000 followed by a parameter k depicting the degrees of freedom. 7 00:00:21,000 --> 00:00:22,320 Therefore, we read the following 8 00:00:22,320 --> 00:00:26,850 as variable Y follows a chi-squared distribution 9 00:00:26,850 --> 00:00:28,350 with three degrees of freedom. 10 00:00:30,000 --> 00:00:31,833 All right, let's get started. 11 00:00:33,240 --> 00:00:37,290 Very few events in real life follow such a distribution. 12 00:00:37,290 --> 00:00:39,510 In fact, chi-squared is most featured 13 00:00:39,510 --> 00:00:42,810 in statistical analysis when doing hypothesis testing 14 00:00:42,810 --> 00:00:44,793 and computing confidence intervals. 15 00:00:45,900 --> 00:00:48,270 In particular, we most commonly find it 16 00:00:48,270 --> 00:00:51,663 when determining the goodness of fit of categorical values. 17 00:00:52,620 --> 00:00:54,660 That is why any example we could give you 18 00:00:54,660 --> 00:00:56,370 would feel extremely convoluted 19 00:00:56,370 --> 00:00:58,893 to anyone not familiar with statistics. 20 00:01:01,140 --> 00:01:03,690 All right, now let's explore the graph 21 00:01:03,690 --> 00:01:05,403 of the chi-squared distribution. 22 00:01:06,990 --> 00:01:09,450 Just by looking at it, you can tell the distribution 23 00:01:09,450 --> 00:01:13,320 is not symmetric, but rather asymmetric. 24 00:01:13,320 --> 00:01:16,080 Its graph is highly skewed to the right. 25 00:01:16,080 --> 00:01:19,290 Furthermore, the values depicted on the x-axis 26 00:01:19,290 --> 00:01:22,023 start from zero rather than a negative number. 27 00:01:23,190 --> 00:01:27,300 This, by the way, shows you yet another transformation. 28 00:01:27,300 --> 00:01:30,630 Elevating the student's T distribution to the second power 29 00:01:30,630 --> 00:01:33,543 gives us the chi-squared, and vice versa. 30 00:01:34,380 --> 00:01:37,620 Finding the square root of the chi-squared distribution 31 00:01:37,620 --> 00:01:39,423 gives us the students t. 32 00:01:41,850 --> 00:01:43,890 Great, so a convenient feature 33 00:01:43,890 --> 00:01:45,660 of the chi-squared distribution 34 00:01:45,660 --> 00:01:48,630 is that it also contains a table of known values, 35 00:01:48,630 --> 00:01:51,723 just like the normal or students T distributions. 36 00:01:53,010 --> 00:01:55,950 The expected value for any chi-squared distribution 37 00:01:55,950 --> 00:01:59,463 is equal to its associated degrees of freedom, k. 38 00:02:00,510 --> 00:02:04,260 Its variance is equal to two times the degrees of freedom, 39 00:02:04,260 --> 00:02:06,273 or simply two times k. 40 00:02:07,950 --> 00:02:09,810 To learn more about hypothesis testing 41 00:02:09,810 --> 00:02:11,130 and confidence intervals, 42 00:02:11,130 --> 00:02:14,567 you can continue with our program where we dive into those. 43 00:02:15,480 --> 00:02:17,490 For now, you know all you need to 44 00:02:17,490 --> 00:02:19,293 about the chi-squared distribution. 45 00:02:20,550 --> 00:02:21,603 Thanks for watching. 3621

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